Influence Of Initial Perturbations Research Articles

Effect of small perturbations on the evolution of polycrystalline structure during plastic deformation

The method of molecular dynamics has been used to study the influence of initial perturbations on the evolution of grain boundaries during the shear plastic deformation of a two-dimensional polycrystalline material with nanoscale grains. It has been shown that short-term thermalization-induced small perturbations result in noticeable differences in grain boundaries configurations at the deformation of 0.05 and the polycrystal completely loses its initial grain boundary structure at the deformation of 0.4.

Simulation and mitigation of the magneto-Rayleigh-Taylor instabilities in Z-pinch gas discharge extreme ultraviolet plasma radiation sources

The development and use of a single-fluid two-temperature approximated 2-D Magneto-Hydrodynamics code is reported. Z-pinch dynamics and the evolution of Magneto-Rayleigh-Taylor (MRT) instabilities in a gas jet type Extreme Ultraviolet (EUV) source are investigated with this code. The implosion and stagnation processes of the Z-pinch dynamics and the influence of initial perturbations (single mode, multi- mode, and random seeds) on MRT instability are discussed in detail. In the case of single mode seeds, the simulation shows that the growth rates for mm-scale wavelengths up to 4 mm are between 0.05 and 0.065 ns−1. For multi-mode seeds, the mode coupling effect leads to a series of other harmonics, and complicates MRT instability evolution. For perturbation by random seeds, the modes evolve to longer wavelengths and finally converge to a mm-scale wavelength approximately 1 mm. MRT instabilities can also alter the pinch stagnation state and lead to temperature and density fluctuations along the Z axis, which eventually affects the homogeneity of the EUV radiation output. Finally, the simulation results are related to experimental results to discuss the mitigations of MRT instability.

Regularizing properties of difference schemes for singular integral-differential equations

Systems of integral-differential equations with a singular matrix multiplying the highest derivative of the unknown vector function are considered. An existence theorem is formulated, and a numerical solution method is proposed. The solutions to singular systems of integral-differential equations are unstable with respect to small perturbations in the initial data. The influence of initial perturbations on the behavior of numerical processes is analyzed. It is shown that the finite-difference schemes proposed for the systems under study are self-regularizing.

Properties of finite-difference schemes for singular integrodifferential equations of index 1

Systems of integrodifferential equations with a singular matrix multiplying the highest derivative of the unknown vector function are considered. An existence theorem is formulated, and a numerical solution method is proposed. The solutions to singular systems of integrodifferential equations are unstable with respect to small perturbations in the initial data. The influence of initial perturbations on the behavior of numerical processes is analyzed. It is shown that the finite-difference schemes proposed for the systems under study are self-regularizing.